Shegelski, Mark

The ideal class group problem is one of the very interesting problems in algebraic number theory. In this thesis we focused on quadratic fields. We studied the group of units of the rings of algebraic integers and calculated fundamental units in several quadratic fields. We also studied a detailed proof of the analytic Dirichlet class number formula with numerical examples and its relation to binary quadratic forms. In addition, we also presented a detailed proof of Carlitz's theorem with numerical examples.

DRAGON seeks to replace its BGO detectors with LaBr3:Ce detectors. The Geant4 simulation estimates gamma ray capture efficiency values of 3.384±0.011% and 1.113±0.007% for the BGO detector and the LaBr3:Ce detector, respectively for 0.6617 MeV gamma rays at 5 cm distance. The latter achieves an experimental efficiency of 1.102±0.042% and an experimental energy resolution of 3.282±0.036% for these gamma rays. The experimental and simulated LaBr3:Ce detector efficiency results agree within error. However, the simulation may overestimate the detector efficiency at high gamma ray energies, as observed at 4.44 MeV and 6.131 MeV. Furthermore, the timing method is performed to utilize its high time resolution. The average resonance energy is 0.47428±0.00815 MeV/u which agrees with the true value of 0.475 MeV/u. Therefore, the energy and time resolution of the LaBr3:Ce detector improve DRAGON’S ability to study radiative capture reactions, with its lower efficiency being its only drawback.

This thesis reviews multiple forms of terahertz spectroscopy and imaging, and exploits a combination of aspects from the techniques involved to undertake a novel method. With the use of this method, subsurface interfaces within a practical, insulated system are spatially imaged and identified. Initially, transmission spectroscopy is used to select the insulating material of the system based on favourable dielectric properties, followed by the use of dove prism reflection spectroscopy to understand and qualitatively contrast the responses of the interfaces to reflecting terahertz pulses. After constructing a reflection imaging system, multiple interface materials concealed by insulation are successfully located and identified by coloured overlays in a 100 by 100 image. Further exploration of applications involving the proposed method is also discussed.

A mixture of waste-wood biomass and municipal biosolids waste was composted in a plastic container inside of an insulated chamber. The mixture of biomass and biosolids was approximately 50:50 and weighed 82.6 kg. The peak temperature of the compost was 32.4◦C. The small scale of the compost system allowed the lower limit of the compost decomposition rate to be studied. A model was successfully developed to predict the core temperature of the compost using the ambient temperature in the insulated chamber. A literature review was conducted to determine literature values for the overall convective and conductive heat transfer coefficient, the dry mass fraction, and heat of combustion for both biomass and biosolids. The model used an optimization algorithm to calculate the rate constant for the experimental setup. The calculated decomposition rate constant was 0.0525 Day−1.